Mathematical modelling of bicarbonate supplementation and acid-base chemistry in kidney failure patients on hemodialysis

Acid-base regulation by the kidneys is largely missing in end-stage renal disease patients undergoing hemodialysis (HD). Bicarbonate is added to the dialysis fluid during HD to replenish the buffers in the body and neutralize interdialytic acid accumulation. Predicting HD outcomes with mathematical models can help select the optimal patient-specific dialysate composition, but the kinetics of bicarbonate are difficult to quantify, because of the many factors involved in the regulation of the bicarbonate buffer in bodily fluids. We implemented a mathematical model of dissolved CO2 and bicarbonate transport that describes the changes in acid-base equilibrium induced by HD to assess the kinetics of bicarbonate, dissolved CO2, and other buffers not only in plasma but also in erythrocytes, interstitial fluid, and tissue cells; the model also includes respiratory control over the partial pressures of CO2 and oxygen. Clinical data were used to fit the model and identify missing parameters used in theoretical simulations. Our results demonstrate the feasibility of the model in describing the changes to acid-base homeostasis typical of HD, and highlight the importance of respiratory regulation during HD.